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Question

If the tangent to the curve y=x3+ax+b at (1, -6) is parallel to the line x - y + 5 = 0, then the value of a - b is .

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Solution

Slope of the line x - y + 5 = 0 is 1. (Comparing with y = mx + c)
Therefore, Slope of the tangent to the curve y=x3+ax+b is also 1.
dydx=3x2+a(dydx)(1,6)=3+aSlope of the given curve at (1,6) is 1.3+a=1a=2 (1,6) lies on the given curve.6=12+bb=5ab=3.

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